Correct Answer - Option 2 : 27
Calculation:
Here, m2- 4mn + 3n2 − 24 = 0
\(\rm ⇒m^2-4mn+(2n)^2-n^2-24=0\)
\(\rm ⇒(m-2n)^2=24+n^2\)
We have, m - 3n = 2 ⇒ m = 3n + 2
\(⇒\rm (3n +2-2n)^2=24+n^2 \)
\(\\⇒ (n+2)^2=24+n^2\)
\(⇒ n^2+4n+4=24+n^2\)
\(\rm ⇒4n=20\)
⇒ n = 5
Putting, value of n in m - 3n = 2, we get
m = 2 + 3(5) = 2 + 15 = 17
∴ (m + 2n) = 17 + 2(5)
= 17 + 10
= 27
Hence, option (3) is correct.